How to turn off reflections on glass
Glass is supposed to be transparent and reflective (and other thing  is refractive, can disperse and absorb light, etc). If you take away the reflections then it will no longer look like glass.
Instead of trying to suppress the reflections, you need to use them to your advantage, so that they feature the characteristics of your object.
Using point lights or very small sources will always result in the kind of ugly spots that you dislike.

That is the very reason why photographers never use point light sources to light shiny objects.
Do an internet search for articles on how to photograph glass and shiny objects. The same principles apply for 3D rendering.
Use large area lights and white panels to light the scene, so that the reflections are much larger and more pleasant (or less distracting). Here's a single very large area light on the same scene: you can see the transparency, reflectiveness, roundness of the object and the overall shape of the object inside the glass.

Delete all the lights you are using, set the world to a black environment, and start with a single large light and play with it, pay attention at what happens with the reflections and the shape of the object, move it and play with the size until you find something that you like, and that suits your needs. Strategically add more lights, or white or black planes, until you get the results you are after.
The same principles that apply to shiny objects can also be used on glass: You are not lighting the object but creating an environment that gets reflected on it.

Read also: Why does an object with a glossy shader render in black?